Problem: You are given three integers a, b, k.

Find two binary integers x and y (x ≥ y) such that 

  1. both x and y consist of a zeroes and b ones; 
  2. x - y (also written in binary form) has exactly k ones. 

You are not allowed to use leading zeros for x and y. 

Input

The only line contains three integers a, b, and k (0 ≤ a; 1 ≤ b; 0 ≤ k ≤ a + b ≤ 2 ⋅ 10^5) — the number of zeroes, ones, and the number of ones in the result.

Output

If it's possible to find two suitable integers, print "Yes" followed by x and y in base-2.

Otherwise print "No".

If there are multiple possible answers, print any of them.

Examples

Input


4 2 3


Output


Yes
101000
100001


Input


3 2 1


Output


Yes
10100
10010


Input


3 2 5


Output


No

Note

In the first example, x = 101000_2 = 2^5 + 2^3 = 40_{10}, y = 100001_2 = 2^5 + 2^0 = 33_{10}, 40_{10} - 33_{10} = 7_{10} = 2^2 + 2^1 + 2^0 = 111_{2}. Hence x-y has 3 ones in base-2.

In the second example, x = 10100_2 = 2^4 + 2^2 = 20_{10}, y = 10010_2 = 2^4 + 2^1 = 18, x - y = 20 - 18 = 2_{10} = 10_{2}. This is precisely one 1.

In the third example, one may show, that it's impossible to find an answer.

Solution (in PYTHON):

Solution:


from __future__ import division, print_function

import os,sys
from io import BytesIO, IOBase

if sys.version_info[0] < 3:
    from __builtin__ import xrange as range
    from future_builtins import ascii, filter, hex, map, oct, zip


# sys.setrecursionlimit(10000000)


def dmain():
    sys.setrecursionlimit(1000000)
    threading.stack_size(1024000)
    thread = threading.Thread(target=main)
    thread.start()
    
#from collections import deque, Counter, OrderedDict,defaultdict
#from heapq import nsmallest, nlargest, heapify,heappop ,heappush, heapreplace
#from math import log,sqrt,factorial,cos,tan,sin,radians
#from bisect import bisect,bisect_left,bisect_right,insort,insort_left,insort_right
#from decimal import *
#import threading
#from itertools import permutations
#Copy 2D list  m = [x[:] for x in mark] .. Avoid Using Deepcopy

# abc='abcdefghijklmnopqrstuvwxyz'
# abd={'a': 0, 'b': 1, 'c': 2, 'd': 3, 'e': 4, 'f': 5, 'g': 6, 'h': 7, 'i': 8, 'j': 9, 'k': 10, 'l': 11, 'm': 12, 'n': 13, 'o': 14, 'p': 15, 'q': 16, 'r': 17, 's': 18, 't': 19, 'u': 20, 'v': 21, 'w': 22, 'x': 23, 'y': 24, 'z': 25}
# mod=1000000007
# #mod=998244353
# inf = float("inf")
# vow=['a','e','i','o','u']
# dx,dy=[-1,1,0,0],[0,0,1,-1]
# def getKey(item): return item[1] 
# def sort2(l):return sorted(l, key=getKey,reverse=True)
# def d2(n,m,num):return [[num for x in range(m)] for y in range(n)]
# def isPowerOfTwo (x): return (x and (not(x & (x - 1))) )
# def decimalToBinary(n): return bin(n).replace("0b","")
# def ntl(n):return [int(i) for i in str(n)]
# def ncr(n,r): return factorial(n)//(factorial(r)*factorial(max(n-r,1)))

# def ceil(x,y):
#     if x%y==0:
#         return x//y
#     else:
#         return x//y+1

# def powerMod(x,y,p):
#     res = 1
#     x %= p
#     while y > 0:
#         if y&1:
#             res = (res*x)%p
#         y = y>>1
#         x = (x*x)%p
#     return res

# def gcd(x, y):
#     while y:
#         x, y = y, x % y
#     return x
    
# def isPrime(n) : # Check Prime Number or not 
#     if (n <= 1) : return False
#     if (n <= 3) : return True
#     if (n % 2 == 0 or n % 3 == 0) : return False
#     i = 5
#     while(i * i <= n) : 
#         if (n % i == 0 or n % (i + 2) == 0) : 
#             return False
#         i = i + 6
#     return True

# def lower_bound(l,k):
#     s = 0
#     e = len(l) - 1
#     while(s<e):
#         m = (s+e)//2
#         if(l[m] >= k):
#             e = m
#         else:
#             s = m+1
#     return s

# def upper_bound(l,k):
#     s = 0
#     e = len(l) - 1
#     while(s<e):
#         m = (s+e)//2
#         if(l[m] <= k):
#             s = m+1
#         else:
#             e = m
#     return s

# def bs(l,k):
#     s = 0
#     e = len(l) - 1
#     while(s<=e):
#         m = (s+e)//2
#         if(l[m] == k):
#             return m
#         elif(l[m] > k):
#             e = m-1
#         else:
#             s = m+1
#     return -1


def read():
    sys.stdin  = open('input.txt', 'r')  
    sys.stdout = open('output.txt', 'w') 


def ii():  return int(input())
def si():  return input()
def mi():  return map(int,input().strip().split(" "))
def msi(): return map(str,input().strip().split(" "))
def li():  return list(mi())


def main():
    # read()
    z,o,k = map(int,input().split())
    if(k==0):
        print("YES")
        print('1'*o + '0'*z)
        print('1'*o + '0'*z)
    elif(z==0 or o==0):
        print("NO")
    elif(z>=1 and o>=2 and k < z+o-1):
        print("YES")
        z -= 1
        o -= 2
        zz = min(k-1, z)
        oo = min(k-1-zz, o)
        a = '1'*(o-oo) + '11' + '0'*zz + '1'*oo + '0' + '0'*(z-zz)
        b = '1'*(o-oo) + '10' + '0'*zz + '1'*oo + '1' + '0'*(z-zz)
        print(a)
        print(b)
    else:
        print("NO")     
        
        








# region fastio
# template taken from https://github.com/cheran-senthil/PyRival/blob/master/templates/template.py

BUFSIZE = 8192


class FastIO(IOBase):
    newlines = 0

    def __init__(self, file):
        self._fd = file.fileno()
        self.buffer = BytesIO()
        self.writable = "x" in file.mode or "r" not in file.mode
        self.write = self.buffer.write if self.writable else None

    def read(self):
        while True:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            if not b:
                break
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines = 0
        return self.buffer.read()

    def readline(self):
        while self.newlines == 0:
            b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
            self.newlines = b.count(b"\n") + (not b)
            ptr = self.buffer.tell()
            self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
        self.newlines -= 1
        return self.buffer.readline()

    def flush(self):
        if self.writable:
            os.write(self._fd, self.buffer.getvalue())
            self.buffer.truncate(0), self.buffer.seek(0)


class IOWrapper(IOBase):
    def __init__(self, file):
        self.buffer = FastIO(file)
        self.flush = self.buffer.flush
        self.writable = self.buffer.writable
        self.write = lambda s: self.buffer.write(s.encode("ascii"))
        self.read = lambda: self.buffer.read().decode("ascii")
        self.readline = lambda: self.buffer.readline().decode("ascii")


def print(*args, **kwargs):
    """Prints the values to a stream, or to sys.stdout by default."""
    sep, file = kwargs.pop("sep", " "), kwargs.pop("file", sys.stdout)
    at_start = True
    for x in args:
        if not at_start:
            file.write(sep)
        file.write(str(x))
        at_start = False
    file.write(kwargs.pop("end", "\n"))
    if kwargs.pop("flush", False):
        file.flush()


if sys.version_info[0] < 3:
    sys.stdin, sys.stdout = FastIO(sys.stdin), FastIO(sys.stdout)
else:
    sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)

input = lambda: sys.stdin.readline().rstrip("\r\n")

# endregion


if __name__ == "__main__":
    
    main()
    # dmain()

# Comment Read()